arXiv 0806.24542008-06math-phgr-qchep-thmath.MP

Noninertial symmetry group with invariant Minkowski line element consistent with Heisenberg quantum commutation relations

Stephen G. Low

备注：: Proceedings of the 28th International Colloquium on Group-Theoretical Methods in Physics, 26-30 July 2010, Newcastle upon Tyne, UK
发表信息：: J.Phys.Conf.Ser.284:012045,2011
DOI：: 10.1088/1742-6596/284/1/012045

英文摘要：

The maximal symmetry of a quantum system with Heisenberg commutation relations is given by the projective representations of the automorphism group of the Weyl-Heisenberg algebra. The automorphism group is the central extension of the inhomogeneous symplectic group with a conformal scaling that acts on extended phase space. We determine the subgroup that also leaves invariant a degenerate orthogonal Minkowski line element. This defines noninertial relativistic symmetry transformations that have the expected classical limit as c becomes infinite.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Projective Representations of the Inhomogeneous Hamilton Group: Noninertial Symmetry in Quantum Mechanics

Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary representations of the central extension of the group. The formulation of the inertial states of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group, and its nonrelativistic limit in terms of the Galilei group, are fundamental examples. Interestingly, neither of these symmetries includes the Weyl-Heisenberg gro…

2011-08-01math-phmath.MPquant-ph

Relativity implications of the quantum phase

The quantum phase leads to projective representations of symmetry groups in quantum mechanics. The projective representations are equivalent to the unitary representations of the central extension of the group. A celebrated example is Wigner's formulation of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group. However, Wigner's formulation makes no mention of the Weyl-Heisenberg group and the hermitian representation of its algebra that are the Heisenberg commutation relations fundamental to quantum physics. We put aside the relativistic …

2011-11-09gr-qcmath-phmath.MP

A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot

We discuss a geometric approach to confining a Dirac neutral particle with a permanent magnetic dipole moment interacting with external fields to a hard-wall confining potential in the Minkowski spacetime through noninertial effects. We discuss the behaviour of external fields induced by noninertial effects, and a case where relativistic bound states can be achieved in analogous way to having a Dirac particle confined to a quantum dot. We show that this confinement of a Dirac neutral particle analogous to a quantum dot arises from noninertial effects that give rise to the geometry of the manif…

2012-10-31cond-mat.mes-hallmath-phmath.MP

Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces

Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace quantizations. These generalized transformations act on deformed superspaces as the ordinary ones do on undeformed spaces but they depend on non(anti)commuting parameters satisfying some consistent (anti)commutation relations. Once the coalgebraic structure compatible with the algebraic one is introduced in the set of transformations we deal with quantum symmetry sup…

2012-03-24hep-thmath-phmath.MP

Wedge Local Deformations of Charged Fields leading to Anyonic Commutation Relations

The method of deforming free fields by using multiplication operators on Fock space, introduced by G. Lechner in [11], is generalized to a charged free field on two- and three-dimensional Minkowski space. In this case the deformation function can be chosen in such a way that the deformed fields satisfy generalized commutation relations, i.e. they behave like Anyons instead of Bosons. The fields are "polarization free" in the sense that they create only one-particle states from the vacuum and they are localized in wedges (or "paths of wedges"), which makes it possible to circumvent a No-Go theo…

2013-01-21hep-thmath-phmath.MP

Local Algebras for Causal Fermion Systems in Minkowski Space

A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the differences to the canonical commutation relations are discussed. It is shown that the spacetime point operators associated to a Cauchy surface satisfy a time slice axiom. It is proven that the algebra generated by operators in an open set is irreducible as a consequence of Hegerfeldt's theorem. The light cone structure is recovered by analyzing expectation values o…

2020-11-16math-phmath.MPmath.OA

更多相关论文收起更多论文

On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT

By invoking the concept of twisted Poincar\' e symmetry of the algebra of functions on a Minkowski space-time, we demonstrate that the noncommutative space-time with the commutation relations $[x_μ,x_ν]=iθ_{μν}$, where $θ_{μν}$ is a {\it constant} real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincaré symmetry on QFT on such a space-time is briefly discussed. The presence of the twisted symmetry gives justification to all the previous treatments within NC QFT using Lorentz invariant quantities and the representations of the usual Poin…

2004-08-13hep-thmath-phmath.MP

Symmetry Reduction of Quasi-Free States

Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry reduced CCR algebra and reduced quasi-free state. When the group is compact this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is non-compact the group averaging prescription relies upon technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein-Gordon field on Minkowski spacetime by …

2009-01-27gr-qchep-thmath-ph

逐点定义的旋量量子场的禁则定理

No-go theorems for pointwise-defined spinorial quantum fields

Centre for Quantum Information and Foundations, DAMTP, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心量子信息与基础中心）

该研究扩展强化了逐点定义量子场的禁则定理，证明弱连续性、费米子微因果性、庞加莱不变分离真空等条件会排除旋量量子场的相关协变性，适用于多种场多重态。

2026-07-30gr-qchep-thmath-ph

$κ$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory

We discuss the obstruction to the construction of a multiparticle field theory on a $κ$-Minkowski noncommutative spacetime: the existence of multilocal functions which respect the deformed symmetries of the problem. This construction is only possible for a light-like version of the commutation relations, if one requires invariance of the tensor product algebra under the coaction of the $κ$-Poincaré group. This necessitates a braided tensor product. We study the representations of this product, and prove that $κ$-Poincaré-invariant N-point functions belong to an Abelian subalgebra, and are ther…

2021-01-24hep-thmath-phmath.MP